Okay, so for this practice exam I\'m doing we are given a density of propane at

Question

Okay, so for this practice exam I'm doing we are given a density of propane at 400K and 30atm from the NIST website. We are then given the a and b values for propane when used with van der waals. We have to determine if the density determined by Van Der Waals is 5% underpredicted when compared with the density from the NIST website. Initially i figured i would just determine the volume with van der waals Equation of State, but that gives me a nasty quadratic which evaluates into a cubic function. I feel like I'm going about this wrong. Is there a better approach?

Explanation / Answer

molar mass of propane = 44

now (P-a/V^2)(V-b) = RT

==> (PV^2-a)(V-b) = RTV^2

==> PV^3 - PbV^2 - aV + ab - RTV^2 = 0

==> PV^3 - (Pb+RT)V^2 - aV + ab = 0

use this site : http://www.1728.org/cubic.htm for solving the cubic in equation

here A = P, B = -(Pb+RT), C = -a, D = ab

you will get three values for this

after that divide the molar mass by V found you will get the density

|(density found - density given)|/density given * 100 = x%

if x is within 5 then it is ok.

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